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Belgarath

rugarch and fGarch

Dear All,

first of all thanks for the great package!

I'm trying to get volatility forecasts. So I tried a couple of packages and I really like the roll functionality provided within the rugarch package but am finding inconsistencies with the results from two garch packages:

1)
I run

GA3=garchFit(formula=~arma(1,0)+aparch(1,1),data=SPX.log.ret,cond.dist="sstd")

modeltofit=ugarchspec(variance.model = list(model = "apARCH", garchOrder = c(1, 1),
submodel = NULL, external.regressors = NULL, variance.targeting = FALSE),
mean.model = list(armaOrder = c(1, 0), include.mean = TRUE, archm = FALSE,
archpow = 1, arfima = FALSE, external.regressors = NULL, archex = FALSE),
distribution.model = "sstd", start.pars = list(), fixed.pars = list())
GAA3=ugarchfit(spec=modeltofit,data=SPX.log.ret)

As you can see from the results below the parameter coefficients are different but similar but the significance is much lower for rugarch. Do you know why?

2)
I then run

volforecast=ugarchroll(spec=modeltofit, data = last(SPX.log.ret,550), n.ahead = 42,
forecast.length = 100, refit.every = 25)
sigma=as.data.frame(volforecast)
sigmat <- as.POSIXct(strptime(sigma[,1],format="%Y-%m-%d"))
sigma2 <- xts(sigma[,3],order.by=sigmat)*100*sqrt(252)

And the results seems to me too low to represent the expected vol in 21 days. Could you please point me in the right direction?

Thank you!

**********************
RESULTS
**********************

fGarch----------------------
> summary(GA3)

Title:
GARCH Modelling

Call:
garchFit(formula = ~arma(1, 0) + aparch(1, 1), data = SPX.log.ret,
cond.dist = "sstd")

Mean and Variance Equation:
data ~ arma(1, 0) + aparch(1, 1)
<environment: 0x000000000c09f038>
[data = SPX.log.ret]

Conditional Distribution:
sstd

Coefficient(s):
mu ar1 omega alpha1 gamma1 beta1
0.00025599 -0.06942414 0.00011829 0.08504516 0.99999999 0.91557956
delta skew shape
1.11700143 0.86337982 5.35586013

Std. Errors:
based on Hessian

Error Analysis:
Estimate Std. Error t value Pr(>|t|)
mu 2.560e-04 2.023e-04 1.266 0.205659
ar1 -6.942e-02 2.332e-02 -2.977 0.002907 **
omega 1.183e-04 3.481e-05 3.399 0.000677 ***
alpha1 8.505e-02 1.285e-02 6.616 3.69e-11 ***
gamma1 1.000e+00 1.441e-02 69.414 < 2e-16 ***
beta1 9.156e-01 1.006e-02 91.041 < 2e-16 ***
delta 1.117e+00 1.962e-01 5.693 1.25e-08 ***
skew 8.634e-01 2.755e-02 31.337 < 2e-16 ***
shape 5.356e+00 8.347e-01 6.416 1.40e-10 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Log Likelihood:
5271.315 normalized: 3.1433

Description:
Tue Jun 12 09:02:05 2012 by user: cora

Standardised Residuals Tests:
Statistic p-Value
Jarque-Bera Test R Chi^2 2459.58 0
Shapiro-Wilk Test R W 0.9528365 0
Ljung-Box Test R Q(10) 11.72432 0.3039307
Ljung-Box Test R Q(15) 15.45374 0.4192542
Ljung-Box Test R Q(20) 21.50983 0.3676896
Ljung-Box Test R^2 Q(10) 90.12559 5.107026e-15
Ljung-Box Test R^2 Q(15) 91.15075 6.047385e-13
Ljung-Box Test R^2 Q(20) 91.74618 3.664247e-11
LM Arch Test R TR^2 26.18211 0.01011463

Information Criterion Statistics:
AIC BIC SIC HQIC
-6.275867 -6.246754 -6.275924 -6.265082

******************************+
******************************

rugarch--------------------
> show(GAA3)

*---------------------------------*
* GARCH Model Fit *
*---------------------------------*

Conditional Variance Dynamics
-----------------------------------
GARCH Model : apARCH(1,1)
Mean Model : ARFIMA(1,0,0)
Distribution : sstd

Optimal Parameters
------------------------------------
Estimate Std. Error t value Pr(>|t|)
mu 0.000237 0.000190 1.2474e+00 0.212265
ar1 -0.069601 0.024100 -2.8881e+00 0.003876
omega 0.000175 0.000148 1.1823e+00 0.237092
alpha1 0.084114 0.011113 7.5687e+00 0.000000
beta1 0.920963 0.009835 9.3640e+01 0.000000
gamma1 1.000000 0.000000 2.6926e+06 0.000000
delta 1.025983 0.159330 6.4393e+00 0.000000
skew 0.860581 0.027580 3.1203e+01 0.000000
shape 5.561683 0.875725 6.3509e+00 0.000000

Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
mu 0.000237 NaN NaN NaN
ar1 -0.069601 NaN NaN NaN
omega 0.000175 NaN NaN NaN
alpha1 0.084114 NaN NaN NaN
beta1 0.920963 NaN NaN NaN
gamma1 1.000000 NaN NaN NaN
delta 1.025983 NaN NaN NaN
skew 0.860581 NaN NaN NaN
shape 5.561683 NaN NaN NaN

LogLikelihood : 5291.85

Information Criteria
------------------------------------

Akaike -6.3004
Bayes -6.2712
Shibata -6.3004
Hannan-Quinn -6.2896

Q-Statistics on Standardized Residuals
------------------------------------
statistic p-value
Lag10 8.594 0.4756
Lag15 13.965 0.4523
Lag20 20.967 0.3386

H0 : No serial correlation

Q-Statistics on Standardized Squared Residuals
------------------------------------
statistic p-value
Lag10 28.13 0.0009072
Lag15 31.84 0.0042245
Lag20 35.40 0.0124798

ARCH LM Tests
------------------------------------
Statistic DoF P-Value
ARCH Lag[2] 12.84 2 0.001630
ARCH Lag[5] 14.26 5 0.014050
ARCH Lag[10] 28.19 10 0.001683

Nyblom stability test
------------------------------------
Joint Statistic: NA
Individual Statistics:
mu 0.90793
ar1 0.11145
omega 0.91076
alpha1 0.53714
beta1 0.60241
gamma1 NA
delta 0.84958
skew 0.06079
shape 0.50963

Asymptotic Critical Values (10% 5% 1%)
Joint Statistic: 2.1 2.32 2.82
Individual Statistic: 0.35 0.47 0.75

Sign Bias Test
------------------------------------
t-value prob sig
Sign Bias 0.7081 0.478964
Negative Sign Bias 2.7958 0.005236 ***
Positive Sign Bias 2.7352 0.006301 ***
Joint Effect 15.8663 0.001208 ***

Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
group statistic p-value(g-1)
1 20 53.65 3.733e-05
2 30 62.55 2.942e-04
3 40 67.52 3.081e-03
4 50 86.60 7.431e-04

Elapsed time : 4.712

alexios

Re: rugarch and fGarch

1. Please examples with reproducible data for such a detailed question.
SPX.log.ret is not a commom data object found in any of the packages I
know of.

2. How is the significance much lower? Looking at the Pr(>|t|) column
they both look very significant across all parameters. The fact that the
robust s.e. have NaN means that the robust hessian could not be
calculated indicating that you need to tune the solver/use scaling (set
'fit.control=list(scale=1)'). Looking at the results, this is likely
because of the 'gamma' parameter hitting its upper limit.

3. This is a rolling out of sample forecast which means that you are
getting rolling estimates using 100 out of sample data points from the
end of your dataset. As to the "expected" vol in 21 days ROLLING 1 day
at a time, 'n.ahead=21', you need to pass this argument to the
as.data.frame method or better still use:
'sigma=as.data.frame(volforecast, which = "sigma")'. This will be
reverting to its long run mean. I really don't know what you expect as
being reasonable or not.

-Alexios

On 12/06/2012 08:49, Belgarath wrote:

> Dear All,
>
> first of all thanks for the great package!
>
> I'm trying to get volatility forecasts. So I tried a couple of packages and
> I really like the roll functionality provided within the rugarch package but
> am finding inconsistencies with the results from two garch packages:
>
> 1)
> I run
>
> GA3=garchFit(formula=~arma(1,0)+aparch(1,1),data=SPX.log.ret,cond.dist="sstd")
>
> modeltofit=ugarchspec(variance.model = list(model = "apARCH", garchOrder =
> c(1, 1),
> submodel = NULL, external.regressors = NULL, variance.targeting = FALSE),
> mean.model = list(armaOrder = c(1, 0), include.mean = TRUE, archm = FALSE,
> archpow = 1, arfima = FALSE, external.regressors = NULL, archex = FALSE),
> distribution.model = "sstd", start.pars = list(), fixed.pars = list())
> GAA3=ugarchfit(spec=modeltofit,data=SPX.log.ret)
>
> As you can see from the results below the parameter coefficients are
> different but similar but the significance is much lower for rugarch. Do you
> know why?
>
> 2)
> I then run
>
> volforecast=ugarchroll(spec=modeltofit, data = last(SPX.log.ret,550),
> n.ahead = 42,
> forecast.length = 100, refit.every = 25)
> sigma=as.data.frame(volforecast)
> sigmat<- as.POSIXct(strptime(sigma[,1],format="%Y-%m-%d"))
> sigma2<- xts(sigma[,3],order.by=sigmat)*100*sqrt(252)
>
> And the results seems to me too low to represent the expected vol in 21
> days. Could you please point me in the right direction?
>
> Thank you!
>
>
>
> **********************
> RESULTS
> **********************
>
>
> fGarch----------------------
>> summary(GA3)
>
> Title:
> GARCH Modelling
>
> Call:
> garchFit(formula = ~arma(1, 0) + aparch(1, 1), data = SPX.log.ret,
> cond.dist = "sstd")
>
> Mean and Variance Equation:
> data ~ arma(1, 0) + aparch(1, 1)
> <environment: 0x000000000c09f038>
> [data = SPX.log.ret]
>
> Conditional Distribution:
> sstd
>
> Coefficient(s):
> mu ar1 omega alpha1 gamma1 beta1
> 0.00025599 -0.06942414 0.00011829 0.08504516 0.99999999 0.91557956
> delta skew shape
> 1.11700143 0.86337982 5.35586013
>
> Std. Errors:
> based on Hessian
>
> Error Analysis:
> Estimate Std. Error t value Pr(>|t|)
> mu 2.560e-04 2.023e-04 1.266 0.205659
> ar1 -6.942e-02 2.332e-02 -2.977 0.002907 **
> omega 1.183e-04 3.481e-05 3.399 0.000677 ***
> alpha1 8.505e-02 1.285e-02 6.616 3.69e-11 ***
> gamma1 1.000e+00 1.441e-02 69.414< 2e-16 ***
> beta1 9.156e-01 1.006e-02 91.041< 2e-16 ***
> delta 1.117e+00 1.962e-01 5.693 1.25e-08 ***
> skew 8.634e-01 2.755e-02 31.337< 2e-16 ***
> shape 5.356e+00 8.347e-01 6.416 1.40e-10 ***
> ---
> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Log Likelihood:
> 5271.315 normalized: 3.1433
>
> Description:
> Tue Jun 12 09:02:05 2012 by user: cora
>
>
> Standardised Residuals Tests:
> Statistic p-Value
> Jarque-Bera Test R Chi^2 2459.58 0
> Shapiro-Wilk Test R W 0.9528365 0
> Ljung-Box Test R Q(10) 11.72432 0.3039307
> Ljung-Box Test R Q(15) 15.45374 0.4192542
> Ljung-Box Test R Q(20) 21.50983 0.3676896
> Ljung-Box Test R^2 Q(10) 90.12559 5.107026e-15
> Ljung-Box Test R^2 Q(15) 91.15075 6.047385e-13
> Ljung-Box Test R^2 Q(20) 91.74618 3.664247e-11
> LM Arch Test R TR^2 26.18211 0.01011463
>
> Information Criterion Statistics:
> AIC BIC SIC HQIC
> -6.275867 -6.246754 -6.275924 -6.265082
>
> ******************************+
> ******************************
>
>
> rugarch--------------------
>> show(GAA3)
>
> *---------------------------------*
> * GARCH Model Fit *
> *---------------------------------*
>
> Conditional Variance Dynamics
> -----------------------------------
> GARCH Model : apARCH(1,1)
> Mean Model : ARFIMA(1,0,0)
> Distribution : sstd
>
> Optimal Parameters
> ------------------------------------
> Estimate Std. Error t value Pr(>|t|)
> mu 0.000237 0.000190 1.2474e+00 0.212265
> ar1 -0.069601 0.024100 -2.8881e+00 0.003876
> omega 0.000175 0.000148 1.1823e+00 0.237092
> alpha1 0.084114 0.011113 7.5687e+00 0.000000
> beta1 0.920963 0.009835 9.3640e+01 0.000000
> gamma1 1.000000 0.000000 2.6926e+06 0.000000
> delta 1.025983 0.159330 6.4393e+00 0.000000
> skew 0.860581 0.027580 3.1203e+01 0.000000
> shape 5.561683 0.875725 6.3509e+00 0.000000
>
> Robust Standard Errors:
> Estimate Std. Error t value Pr(>|t|)
> mu 0.000237 NaN NaN NaN
> ar1 -0.069601 NaN NaN NaN
> omega 0.000175 NaN NaN NaN
> alpha1 0.084114 NaN NaN NaN
> beta1 0.920963 NaN NaN NaN
> gamma1 1.000000 NaN NaN NaN
> delta 1.025983 NaN NaN NaN
> skew 0.860581 NaN NaN NaN
> shape 5.561683 NaN NaN NaN
>
> LogLikelihood : 5291.85
>
> Information Criteria
> ------------------------------------
>
> Akaike -6.3004
> Bayes -6.2712
> Shibata -6.3004
> Hannan-Quinn -6.2896
>
> Q-Statistics on Standardized Residuals
> ------------------------------------
> statistic p-value
> Lag10 8.594 0.4756
> Lag15 13.965 0.4523
> Lag20 20.967 0.3386
>
> H0 : No serial correlation
>
> Q-Statistics on Standardized Squared Residuals
> ------------------------------------
> statistic p-value
> Lag10 28.13 0.0009072
> Lag15 31.84 0.0042245
> Lag20 35.40 0.0124798
>
> ARCH LM Tests
> ------------------------------------
> Statistic DoF P-Value
> ARCH Lag[2] 12.84 2 0.001630
> ARCH Lag[5] 14.26 5 0.014050
> ARCH Lag[10] 28.19 10 0.001683
>
> Nyblom stability test
> ------------------------------------
> Joint Statistic: NA
> Individual Statistics:
> mu 0.90793
> ar1 0.11145
> omega 0.91076
> alpha1 0.53714
> beta1 0.60241
> gamma1 NA
> delta 0.84958
> skew 0.06079
> shape 0.50963
>
> Asymptotic Critical Values (10% 5% 1%)
> Joint Statistic: 2.1 2.32 2.82
> Individual Statistic: 0.35 0.47 0.75
>
> Sign Bias Test
> ------------------------------------
> t-value prob sig
> Sign Bias 0.7081 0.478964
> Negative Sign Bias 2.7958 0.005236 ***
> Positive Sign Bias 2.7352 0.006301 ***
> Joint Effect 15.8663 0.001208 ***
>
>
> Adjusted Pearson Goodness-of-Fit Test:
> ------------------------------------
> group statistic p-value(g-1)
> 1 20 53.65 3.733e-05
> 2 30 62.55 2.942e-04
> 3 40 67.52 3.081e-03
> 4 50 86.60 7.431e-04
>
>
> Elapsed time : 4.712
>
> --
> View this message in context: http://r.789695.n4.nabble.com/rugarch-and-fGarch-tp4633077.html
> Sent from the Rmetrics mailing list archive at Nabble.com.
>
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Belgarath

Re: rugarch and fGarch

Hello Alexios,

thank you for the quick reply! Apologies but yesterday yahoo finance was not working so could not follow up with an appropriate reproducible example:

1)
----
getSymbols("^GSPC", src="yahoo")
SPY.log.ret=ClCl(GSPC)
GA3=garchFit(formula=~arma(1,0)+aparch(1,1),data=last(SPY.log.ret,1371),cond.dist="sstd")
summary(GA3)
modeltofit=ugarchspec(variance.model = list(model = "apARCH", garchOrder = c(1, 1),
submodel = NULL, external.regressors = NULL, variance.targeting = FALSE),
mean.model = list(armaOrder = c(1, 0), include.mean = TRUE, archm = FALSE,
archpow = 1, arfima = FALSE, external.regressors = NULL, archex = FALSE),
distribution.model = "sstd", start.pars = list(), fixed.pars = list())

GAA3=ugarchfit(spec=modeltofit,data=last(SPY.log.ret,1371))
show(GAA3)
volforecast=ugarchroll(spec=modeltofit,data=last(SPY.log.ret,1371), n.ahead = 21,
forecast.length = 420, refit.every = 21)
sigma=as.data.frame(volforecast,which="density",n.ahead=21)
sigmat <- as.POSIXct(strptime(sigma[,1],format="%Y-%m-%d"))
sigma2 <- xts(sigma[,3],order.by=sigmat)*100*sqrt(252)
plot(sigma2)
---

Detailed results are below, but to reply to your points:
2) rugarch omega is 0.000618 t:1.5062e+00 p:0.132023 while fGarch omega is 3.922e-04 t:3.970 p:7.19e-05 which is more significant.

3) Is the code above usage correct to extract the forecasts? I tried to use the sigma=as.data.frame(volforecast, which = "sigma") but it only return the first 21 forecasts. How do I extract the long term mean of the st dev?

4) I have one more question: the dates in the sigma=as.data.frame(volforecast,which="density",n.ahead=21) are alligned with the date the forecast refers to no the date the forcast is made (ie. it will be delayed by 21 days in a chart) correct?

Thank you again for the help and the package!
Marco

*****************
> show(GAA3)

*---------------------------------*
* GARCH Model Fit *
*---------------------------------*

Conditional Variance Dynamics
-----------------------------------
GARCH Model : apARCH(1,1)
Mean Model : ARFIMA(1,0,0)
Distribution : sstd

Optimal Parameters
------------------------------------
Estimate Std. Error t value Pr(>|t|)
mu 0.000197 0.000007 2.7154e+01 0.000000
ar1 -0.086149 0.000122 -7.0664e+02 0.000000
omega 0.000618 0.000411 1.5062e+00 0.132023
alpha1 0.090424 0.010405 8.6908e+00 0.000000
beta1 0.916128 0.010687 8.5724e+01 0.000000
gamma1 1.000000 0.000000 2.5738e+06 0.000000
delta 0.844145 0.130924 6.4476e+00 0.000000
skew 0.833679 0.028852 2.8895e+01 0.000000
shape 7.325115 1.542399 4.7492e+00 0.000002

Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
mu 0.000197 NaN NaN NaN
ar1 -0.086149 NaN NaN NaN
omega 0.000618 NaN NaN NaN
alpha1 0.090424 NaN NaN NaN
beta1 0.916128 NaN NaN NaN
gamma1 1.000000 NaN NaN NaN
delta 0.844145 NaN NaN NaN
skew 0.833679 NaN NaN NaN
shape 7.325115 NaN NaN NaN

LogLikelihood : 4133.434

Information Criteria
------------------------------------

Akaike -6.0167
Bayes -5.9824
Shibata -6.0168
Hannan-Quinn -6.0038

Q-Statistics on Standardized Residuals
------------------------------------
statistic p-value
Lag10 11.45 0.2459
Lag15 16.60 0.2780
Lag20 18.74 0.4737

H0 : No serial correlation

Q-Statistics on Standardized Squared Residuals
------------------------------------
statistic p-value
Lag10 29.72 0.0004892
Lag15 33.15 0.0027369
Lag20 36.37 0.0094979

ARCH LM Tests
------------------------------------
Statistic DoF P-Value
ARCH Lag[2] 15.81 2 0.0003695
ARCH Lag[5] 16.98 5 0.0045286
ARCH Lag[10] 30.99 10 0.0005890

Nyblom stability test
------------------------------------
Joint Statistic: NA
Individual Statistics:
mu 0.2380
ar1 0.2163
omega 0.1923
alpha1 0.1939
beta1 0.2190
gamma1 NA
delta 0.2084
skew 0.1054
shape 0.2543

Asymptotic Critical Values (10% 5% 1%)
Joint Statistic: 2.1 2.32 2.82
Individual Statistic: 0.35 0.47 0.75

Sign Bias Test
------------------------------------
t-value prob sig
Sign Bias 0.3575 0.720737
Negative Sign Bias 2.5732 0.010180 **
Positive Sign Bias 2.7813 0.005489 ***
Joint Effect 14.4861 0.002313 ***

Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
group statistic p-value(g-1)
1 20 30.47 0.046075
2 30 40.31 0.078949
3 40 54.67 0.049050
4 50 74.99 0.009861

Elapsed time : 5.466

> summary(GA3)

Title:
GARCH Modelling

Call:
garchFit(formula = ~arma(1, 0) + aparch(1, 1), data = last(SPY.log.ret,
1371), cond.dist = "sstd")

Mean and Variance Equation:
data ~ arma(1, 0) + aparch(1, 1)
<environment: 0x000000000e8e8e68>
[data = last(SPY.log.ret, 1371)]

Conditional Distribution:
sstd

Coefficient(s):
mu ar1 omega alpha1 gamma1 beta1
0.00022015 -0.08726888 0.00039220 0.09300673 0.99999999 0.90917036
delta skew shape
0.95108469 0.83598044 7.13436954

Std. Errors:
based on Hessian

Error Analysis:
Estimate Std. Error t value Pr(>|t|)
mu 2.202e-04 2.702e-04 0.815 0.415301
ar1 -8.727e-02 2.557e-02 -3.413 0.000643 ***
omega 3.922e-04 9.879e-05 3.970 7.19e-05 ***
alpha1 9.301e-02 1.157e-02 8.035 8.88e-16 ***
gamma1 1.000e+00 1.085e-02 92.183 < 2e-16 ***
beta1 9.092e-01 1.112e-02 81.759 < 2e-16 ***
delta 9.511e-01 1.667e-01 5.705 1.16e-08 ***
skew 8.360e-01 3.064e-02 27.284 < 2e-16 ***
shape 7.134e+00 1.543e+00 4.625 3.75e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Log Likelihood:
4131.182 normalized: 3.013262

Description:
Wed Jun 13 14:57:49 2012 by user: cora

Standardised Residuals Tests:
Statistic p-Value
Jarque-Bera Test R Chi^2 1584.761 0
Shapiro-Wilk Test R W 0.9597795 0
Ljung-Box Test R Q(10) 12.32339 0.2639963
Ljung-Box Test R Q(15) 16.8469 0.3280988
Ljung-Box Test R Q(20) 18.48151 0.5557211
Ljung-Box Test R^2 Q(10) 9.478356 0.4873852
Ljung-Box Test R^2 Q(15) 12.33782 0.6532996
Ljung-Box Test R^2 Q(20) 13.34997 0.8618686
LM Arch Test R TR^2 29.52316 0.003292551

Information Criterion Statistics:
AIC BIC SIC HQIC
-6.013395 -5.979106 -6.013480 -6.000563

alexios

Re: rugarch and fGarch

Marco,

1. Use:
GAA3=ugarchfit(spec=modeltofit,data=last(SPY.log.ret,1371),
fit.control=list(scale=1))
This should get a better result so that the evaluation of the robust
estimates does not fail.

2. Likelihoods are very close but omega and their s.e. is somewhat
different.

To better compare the results use the coefficients from the 2 fits in
rugarch:

spec1 = modeltofit
setfixed(spec1)<-as.list(coef(GA3))
spec2 = modeltofit
setfixed(spec2)<-as.list(coef(GAA3))

fit1 = ugarchfit(spec1, last(SPY.log.ret,1371),
fit.control=list(fixed.se=1))

fit2 = ugarchfit(spec2, last(SPY.log.ret,1371),
fit.control=list(fixed.se=1))

round(cbind(coef(fit1), coef(fit2)),4)
fGarch rugarch
mu 0.0002 0.0002
ar1 -0.0873 -0.0861
omega 0.0004 0.0006
alpha1 0.0930 0.0904
beta1 0.9092 0.9161
gamma1 1.0000 1.0000
delta 0.9511 0.8431
skew 0.8360 0.8337
shape 7.1344 7.3343

Look at their long run sigma:
sqrt(uncvariance(fit1))
0.01391264

sqrt(uncvariance(fit2))
0.01378647

As i said in the earlier email, differences are likely related to the
gamma parameter hitting its limit, but will investigate some alternate
strategies for the omega coefficient scaling when time permits.

3. I don't really understand what you want to do. If you just want the
long run unconditional forecast then extract the coefficients from each fit:

cf = as.data.frame(volforecast, which = "coefmat", refit=2)
cfnames = rownames(cf)
cf = cf[,1]
names(cf)=cfnames
spec = modeltofit
setfixed(spec)<-as.list(cf)
uncvariance(spec)

sigma=as.data.frame(volforecast,which="sigma")

Is correct. It returns a n.ahead x n.roll matrix.
For the time being, it only support n.ahead<=refit.every.

If you want to create long run custom type forecasts just wrap your own
ugarchfit+ugarchforecast function (after all that is all that ugarchroll
does). Read the documentation on the proper use of the "out.sample" option.

4. NO. The forecast date shown is the ACTUAL future forecast date (since
this is an out.of sample rolling forecast for which dates exists). In
the ugarchforecast method, when there are no out.sample dates to draw
from, the program generates actual future forecast dates (not taking
into account holidays etc).

-Alexios

On 13/06/2012 14:13, Belgarath wrote:

> Hello Alexios,
>
> thank you for the quick reply! Apologies but yesterday yahoo finance was not
> working so could not follow up with an appropriate reproducible example:
>
> 1)
> ----
> getSymbols("^GSPC", src="yahoo")
> SPY.log.ret=ClCl(GSPC)
> GA3=garchFit(formula=~arma(1,0)+aparch(1,1),data=last(SPY.log.ret,1371),cond.dist="sstd")
> summary(GA3)
> modeltofit=ugarchspec(variance.model = list(model = "apARCH", garchOrder =
> c(1, 1),
> submodel = NULL, external.regressors = NULL,
> variance.targeting = FALSE),
> mean.model = list(armaOrder = c(1, 0), include.mean =
> TRUE, archm = FALSE,
> archpow = 1, arfima = FALSE, external.regressors = NULL,
> archex = FALSE),
> distribution.model = "sstd", start.pars = list(),
> fixed.pars = list())
>
> GAA3=ugarchfit(spec=modeltofit,data=last(SPY.log.ret,1371))
> show(GAA3)
> volforecast=ugarchroll(spec=modeltofit,data=last(SPY.log.ret,1371), n.ahead
> = 21,
> forecast.length = 420, refit.every = 21)
> sigma=as.data.frame(volforecast,which="density",n.ahead=21)
> sigmat <- as.POSIXct(strptime(sigma[,1],format="%Y-%m-%d"))
> sigma2 <- xts(sigma[,3],order.by=sigmat)*100*sqrt(252)
> plot(sigma2)
> ---
>
> Detailed results are below, but to reply to your points:
> 2) rugarch omega is 0.000618 t:1.5062e+00 p:0.132023 while fGarch omega
> is 3.922e-04 t:3.970 p:7.19e-05 which is more significant.
>
> 3) Is the code above usage correct to extract the forecasts? I tried to use
> the sigma=as.data.frame(volforecast, which = "sigma") but it only return the
> first 21 forecasts. How do I extract the long term mean of the st dev?
>
> 4) I have one more question: the dates in the
> sigma=as.data.frame(volforecast,which="density",n.ahead=21) are alligned
> with the date the forecast refers to no the date the forcast is made (ie. it
> will be delayed by 21 days in a chart) correct?
>
> Thank you again for the help and the package!
> Marco
>
>
>
> *****************
>> show(GAA3)
>
> *---------------------------------*
> * GARCH Model Fit *
> *---------------------------------*
>
> Conditional Variance Dynamics
> -----------------------------------
> GARCH Model : apARCH(1,1)
> Mean Model : ARFIMA(1,0,0)
> Distribution : sstd
>
> Optimal Parameters
> ------------------------------------
> Estimate Std. Error t value Pr(>|t|)
> mu 0.000197 0.000007 2.7154e+01 0.000000
> ar1 -0.086149 0.000122 -7.0664e+02 0.000000
> omega 0.000618 0.000411 1.5062e+00 0.132023
> alpha1 0.090424 0.010405 8.6908e+00 0.000000
> beta1 0.916128 0.010687 8.5724e+01 0.000000
> gamma1 1.000000 0.000000 2.5738e+06 0.000000
> delta 0.844145 0.130924 6.4476e+00 0.000000
> skew 0.833679 0.028852 2.8895e+01 0.000000
> shape 7.325115 1.542399 4.7492e+00 0.000002
>
> Robust Standard Errors:
> Estimate Std. Error t value Pr(>|t|)
> mu 0.000197 NaN NaN NaN
> ar1 -0.086149 NaN NaN NaN
> omega 0.000618 NaN NaN NaN
> alpha1 0.090424 NaN NaN NaN
> beta1 0.916128 NaN NaN NaN
> gamma1 1.000000 NaN NaN NaN
> delta 0.844145 NaN NaN NaN
> skew 0.833679 NaN NaN NaN
> shape 7.325115 NaN NaN NaN
>
> LogLikelihood : 4133.434
>
> Information Criteria
> ------------------------------------
>
> Akaike -6.0167
> Bayes -5.9824
> Shibata -6.0168
> Hannan-Quinn -6.0038
>
> Q-Statistics on Standardized Residuals
> ------------------------------------
> statistic p-value
> Lag10 11.45 0.2459
> Lag15 16.60 0.2780
> Lag20 18.74 0.4737
>
> H0 : No serial correlation
>
> Q-Statistics on Standardized Squared Residuals
> ------------------------------------
> statistic p-value
> Lag10 29.72 0.0004892
> Lag15 33.15 0.0027369
> Lag20 36.37 0.0094979
>
> ARCH LM Tests
> ------------------------------------
> Statistic DoF P-Value
> ARCH Lag[2] 15.81 2 0.0003695
> ARCH Lag[5] 16.98 5 0.0045286
> ARCH Lag[10] 30.99 10 0.0005890
>
> Nyblom stability test
> ------------------------------------
> Joint Statistic: NA
> Individual Statistics:
> mu 0.2380
> ar1 0.2163
> omega 0.1923
> alpha1 0.1939
> beta1 0.2190
> gamma1 NA
> delta 0.2084
> skew 0.1054
> shape 0.2543
>
> Asymptotic Critical Values (10% 5% 1%)
> Joint Statistic: 2.1 2.32 2.82
> Individual Statistic: 0.35 0.47 0.75
>
> Sign Bias Test
> ------------------------------------
> t-value prob sig
> Sign Bias 0.3575 0.720737
> Negative Sign Bias 2.5732 0.010180 **
> Positive Sign Bias 2.7813 0.005489 ***
> Joint Effect 14.4861 0.002313 ***
>
>
> Adjusted Pearson Goodness-of-Fit Test:
> ------------------------------------
> group statistic p-value(g-1)
> 1 20 30.47 0.046075
> 2 30 40.31 0.078949
> 3 40 54.67 0.049050
> 4 50 74.99 0.009861
>
>
> Elapsed time : 5.466
>
>> summary(GA3)
>
> Title:
> GARCH Modelling
>
> Call:
> garchFit(formula = ~arma(1, 0) + aparch(1, 1), data = last(SPY.log.ret,
> 1371), cond.dist = "sstd")
>
> Mean and Variance Equation:
> data ~ arma(1, 0) + aparch(1, 1)
> <environment: 0x000000000e8e8e68>
> [data = last(SPY.log.ret, 1371)]
>
> Conditional Distribution:
> sstd
>
> Coefficient(s):
> mu ar1 omega alpha1 gamma1 beta1
> 0.00022015 -0.08726888 0.00039220 0.09300673 0.99999999 0.90917036
> delta skew shape
> 0.95108469 0.83598044 7.13436954
>
> Std. Errors:
> based on Hessian
>
> Error Analysis:
> Estimate Std. Error t value Pr(>|t|)
> mu 2.202e-04 2.702e-04 0.815 0.415301
> ar1 -8.727e-02 2.557e-02 -3.413 0.000643 ***
> omega 3.922e-04 9.879e-05 3.970 7.19e-05 ***
> alpha1 9.301e-02 1.157e-02 8.035 8.88e-16 ***
> gamma1 1.000e+00 1.085e-02 92.183 < 2e-16 ***
> beta1 9.092e-01 1.112e-02 81.759 < 2e-16 ***
> delta 9.511e-01 1.667e-01 5.705 1.16e-08 ***
> skew 8.360e-01 3.064e-02 27.284 < 2e-16 ***
> shape 7.134e+00 1.543e+00 4.625 3.75e-06 ***
> ---
> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Log Likelihood:
> 4131.182 normalized: 3.013262
>
> Description:
> Wed Jun 13 14:57:49 2012 by user: cora
>
>
> Standardised Residuals Tests:
> Statistic p-Value
> Jarque-Bera Test R Chi^2 1584.761 0
> Shapiro-Wilk Test R W 0.9597795 0
> Ljung-Box Test R Q(10) 12.32339 0.2639963
> Ljung-Box Test R Q(15) 16.8469 0.3280988
> Ljung-Box Test R Q(20) 18.48151 0.5557211
> Ljung-Box Test R^2 Q(10) 9.478356 0.4873852
> Ljung-Box Test R^2 Q(15) 12.33782 0.6532996
> Ljung-Box Test R^2 Q(20) 13.34997 0.8618686
> LM Arch Test R TR^2 29.52316 0.003292551
>
> Information Criterion Statistics:
> AIC BIC SIC HQIC
> -6.013395 -5.979106 -6.013480 -6.000563
>
>
>
> --
> View this message in context: http://r.789695.n4.nabble.com/rugarch-and-fGarch-tp4633077p4633253.html
> Sent from the Rmetrics mailing list archive at Nabble.com.
>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
> -- Subscriber-posting only. If you want to post, subscribe first.
> -- Also note that this is not the r-help list where general R questions should go.
>

Belgarath

Re: rugarch and fGarch

Hello Alexios,

thank you very much!

With the fit.control=list(scale=1) is also much faster.

I also added the multi-core support, is there any other way to improve the performance?

Thank you very much!
Marco

alexios

Re: rugarch and fGarch

Marco,

All models (more precisely their filters which are used in the
estimation process) in the rugarch package are already coded in C for speed.
The "apARCH" is an omnibus model and as such carries a penalty for such
flexibility, as does the use of the 'sstd' distribution.
There is also a small penalty for the 1-stage estimation of
ARFIMA-GARCH, rather than the marginally faster 2 stage estimation which
I do not make use of in the package (but you can control for that by
passing an arima filtered residual series using an appropriate
specification and reconstituting later with fixed parameters in the spec
for doing forecasting).
For the rolling estimation, you can make use of the parallel option to
evaluate in parallel the rolling estimations/forecasts. See the FAQ
section of the vignette for some comments on the tradeoff between the
number of cores to use versus the size of the problem for the snowfall
package. I have personally found that running things on linux with the
multicore package is quite faster, but that may be because I do not have
any optimized setup for windows R.

-Alexios

On 14/06/2012 13:23, Belgarath wrote:

> Hello Alexios,
>
> thank you very much!
>
> With the fit.control=list(scale=1) is also much faster.
>
> I also added the multi-core support, is there any other way to improve the
> performance?
>
> Thank you very much!
> Marco
>
> --
> View this message in context: http://r.789695.n4.nabble.com/rugarch-and-fGarch-tp4633077p4633368.html
> Sent from the Rmetrics mailing list archive at Nabble.com.
>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
> -- Subscriber-posting only. If you want to post, subscribe first.
> -- Also note that this is not the r-help list where general R questions should go.
>

Belgarath

Re: rugarch and fGarch

Thank you very much Alexios.

One more question, related to my point (4) two messages above, where I probably have not been very clear. Please see the following code.

---
getSymbols("^GSPC", src="yahoo")
getSymbols("^VIX", src="yahoo")
SPY.log.ret=ClCl(GSPC)
#GA3=garchFit(formula=~arma(1,0)+aparch(1,1),data=last(SPY.log.ret,1371),cond.dist="sstd")
#summary(GA3)
modeltofit=ugarchspec(variance.model = list(model = "apARCH", garchOrder = c(1, 1),
submodel = NULL, external.regressors = NULL, variance.targeting = FALSE),
mean.model = list(armaOrder = c(1, 0), include.mean = TRUE, archm = FALSE,
archpow = 1, arfima = FALSE, external.regressors = NULL, archex = FALSE),
distribution.model = "sstd", start.pars = list(), fixed.pars = list())

#GAA3=ugarchfit(spec=modeltofit,data=last(SPY.log.ret,1371),fit.control=list(scale=1))
#show(GAA3)
volforecast=ugarchroll(spec=modeltofit,data=last(SPY.log.ret,1371), n.ahead = 21,
forecast.length = 420, refit.every = 21,
fit.control=list(scale=1))
sigma=as.data.frame(volforecast,which="density",n.ahead=21)
sigmat <- as.Date(strptime(sigma[,1],format="%Y-%m-%d"))
sigma2 <- xts(sigma[,3],order.by=sigmat)*100*sqrt(252)
plot(sigma2)
lines(Cl(VIX), col="red")

sigmat <- as.Date(index(first(last(GSPC,420+21),420)))
sigma2 <- xts(sigma[,3],order.by=sigmat)*100*sqrt(252)

plot(sigma2)
lines(Cl(VIX), col="red")

---

As you can see the two are very distant: I think the dates that are passed by the as.data.frame(volforecast,which="density",n.ahead=21) refers to the forecast date (i.e. 2012-05-07 20.7 means the vol is forecasted to be 20.7 on the 2012-05-07) not the date in which the forecast is made (i.e. the forecast for the 21d vol made on the 2012-05-07 is 20.7). I realise I was not very clear in my previous question...

So if I instead use

---
sigmat2 <- as.Date(index(first(last(GSPC,420+21),420)))
sigma3 <- xts(sigma[,3],order.by=sigmat)*100*sqrt(252)

plot(sigma3)
lines(Cl(VIX), col="red")

----

they are now aligned.

So if I want the 21d forecast aligned with the date they have been made I have to go for the second version, correct?

In this way thou I missed the last 21 days in the sample, do you think there is a way to get them back?

Thank you very much for all the help!
Rgds,
marco

alexios

Re: rugarch and fGarch

Please try to make the reproducible examples a little more compact.

As I said in the previous email the dates shown are the dates aligned to
the n.ahead forecast. The fact that you do not get the last 21 days is
because the rolling method uses only out.sample data i.e. forecasts only
up to the available out.sample (see the ugarchforecast function).
I also mentioned that n.ahead MUST BE <= refit.every (i.e.
n.ahead<=out.sample per refit), and that a change to accommodate the
case of n.ahead>refit.every might come in due course.
The point of using the rolling function is for backtesting models for
which you need realized (i.e. out.sample) data to do so. I will again
urge you to wrap your own function which makes use of the
ugarchfit+ugarchforecast functions if you want more customization.

-Alexios

On 14/06/2012 19:07, Belgarath wrote:

> Thank you very much Alexios.
>
> One more question, related to my point (4) two messages above, where I
> probably have not been very clear. Please see the following code.
>
> ---
> getSymbols("^GSPC", src="yahoo")
> getSymbols("^VIX", src="yahoo")
> SPY.log.ret=ClCl(GSPC)
> #GA3=garchFit(formula=~arma(1,0)+aparch(1,1),data=last(SPY.log.ret,1371),cond.dist="sstd")
> #summary(GA3)
> modeltofit=ugarchspec(variance.model = list(model = "apARCH", garchOrder =
> c(1, 1),
> submodel = NULL, external.regressors = NULL,
> variance.targeting = FALSE),
> mean.model = list(armaOrder = c(1, 0), include.mean =
> TRUE, archm = FALSE,
> archpow = 1, arfima = FALSE, external.regressors = NULL,
> archex = FALSE),
> distribution.model = "sstd", start.pars = list(),
> fixed.pars = list())
>
> #GAA3=ugarchfit(spec=modeltofit,data=last(SPY.log.ret,1371),fit.control=list(scale=1))
> #show(GAA3)
> volforecast=ugarchroll(spec=modeltofit,data=last(SPY.log.ret,1371), n.ahead
> = 21,
> forecast.length = 420, refit.every = 21,
> fit.control=list(scale=1))
> sigma=as.data.frame(volforecast,which="density",n.ahead=21)
> sigmat <- as.Date(strptime(sigma[,1],format="%Y-%m-%d"))
> sigma2 <- xts(sigma[,3],order.by=sigmat)*100*sqrt(252)
> plot(sigma2)
> lines(Cl(VIX), col="red")
>
> sigmat <- as.Date(index(first(last(GSPC,420+21),420)))
> sigma2 <- xts(sigma[,3],order.by=sigmat)*100*sqrt(252)
>
> plot(sigma2)
> lines(Cl(VIX), col="red")
>
> ---
>
> As you can see the two are very distant: I think the dates that are passed
> by the as.data.frame(volforecast,which="density",n.ahead=21) refers to the
> forecast date (i.e. 2012-05-07 20.7 means the vol is forecasted to be
> 20.7 on the 2012-05-07) not the date in which the forecast is made (i.e. the
> forecast for the 21d vol made on the 2012-05-07 is 20.7). I realise I was
> not very clear in my previous question...
>
> So if I instead use
>
> ---
> sigmat2 <- as.Date(index(first(last(GSPC,420+21),420)))
> sigma3 <- xts(sigma[,3],order.by=sigmat)*100*sqrt(252)
>
> plot(sigma3)
> lines(Cl(VIX), col="red")
>
> ----
>
> they are now aligned.
>
> So if I want the 21d forecast aligned with the date they have been made I
> have to go for the second version, correct?
>
> In this way thou I missed the last 21 days in the sample, do you think there
> is a way to get them back?
>
> Thank you very much for all the help!
> Rgds,
> marco
>
>
>
>
>
>
>
>
> --
> View this message in context: http://r.789695.n4.nabble.com/rugarch-and-fGarch-tp4633077p4633432.html
> Sent from the Rmetrics mailing list archive at Nabble.com.
>
> _______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
> -- Subscriber-posting only. If you want to post, subscribe first.
> -- Also note that this is not the r-help list where general R questions should go.
>